MIMO system method and device using sorted QR-decomposition (SQRD) for detecting transmission signal with division detection

ABSTRACT

The present invention relates to a method and device for detecting a transmission signal on the basis of a received signal by applying a division and detection algorithm. An embodiment of the invention provides a method of detecting a transmission signal including: obtaining a unitary matrix and an upper triangular matrix by performing a sorted QR-decomposition algorithm with respect to a matrix indicating a channel state; calculating a vector y by multiplying a transpose matrix of the unitary matrix by the received signal Y; dividing the upper triangular matrix R into a plurality of sub-upper triangular matrices and dividing the calculated vector y into a plurality of sub-vectors so as to correspond to the divided plurality of sub-upper triangular matrices; and detecting a lattice point corresponding to each of the divided sub-vectors using the divided plurality of sub-upper triangular matrices.

BACKGROUND OF THE INVENTION

(a) Field of the Invention

The present invention relates to a transmission signal detection methodand device using division detection. In particular, the presentinvention relates to an adaptive transmission signal detection methodand device that are capable of sufficiently reducing error probabilityof a detected signal and simultaneously reducing an amount ofcalculation when a transmission signal vector is detected from areceived signal vector corresponding to a transmission signal vectorthat includes a plurality of signals and uses high modulation, and thenumber of signals included in the received signal vector and thetransmission signal vector is large.

(b) Description of the Related Art

A receiving terminal of a communication system detects a transmissionsignal vector X having M complex numbers from a signal vector Y having Ncomplex numbers measured in the receiving terminal, wherein thetransmission signal vector X should be close to an original signal.

Generally, the vector Y is the same as a vector obtained by multiplyingthe vector X by an N×M matrix and then adding a noise vector to themultiplied value.

The N×M matrix to be multiplied by the vector X is a matrix that isassumed and known in the receiving terminal, and the noise vector isassumed to be Gaussian noise.

If a signal constellation used in the transmission is 2Q-QAM, eachelement included in the X is included in the 2Q-QAM. When the vector Xis obtained by using a maximum likelihood detection method which isknown to have the best performance as a signal detection method, anumber of multiplications required is at least N×(M+1)×2^(M×Q).

Furthermore, when a log likelihood ratio (LLR) is calculated in order tocalculate an input value of a channel decoder, the number ofmultiplications required is

$\frac{3}{2} \times N \times \left( {M + 1} \right) \times {2^{M \times Q}.}$

Therefore, when the values of M and Q become large, the amount ofcalculation increases in geometric progression, and there is a drawbackin that it is difficult to apply to a system.

In order to cope with the drawback, methods of performing calculation ina local range where the maximum likelihood point is expected to existhave been proposed in recent years.

One of the representative methods is a sphere decoding method. Asanother access method, a QRM-MLD (QR decomposition and M-algorithm)method is proposed. The QRM-MLD method has performance that is close tothe maximum likelihood detection.

However, those proposed methods have limits in improving the complexityof the calculation when a number of signals are included in the receivedsignal vector and the transmission signal vector.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY OF THE INVENTION

The present invention has been made in an effort to provide a method fordetecting a transmission signal from a received signal and a devicethereof having advantages of securing a signal detection performanceequal to or higher than a predetermined level and reducing thecomplexity of a calculation process for simultaneous signal detection byconsidering an amount of calculation for a signal detection performancein a multiple input multiple output (MIMO) system.

An exemplary embodiment of the present invention provides a method ofdetecting a transmission signal from a received signal in an MIMOsystem, the method including: obtaining a unitary matrix Q and an uppertriangular matrix R by performing a sorted QR-decomposition (SQRD)algorithm with respect to a matrix B indicating a channel state;calculating a vector y by multiplying an transpose matrix Q^(t) of theunitary matrix Q by the received signal Y; dividing the upper triangularmatrix R into a plurality of sub-upper triangular matrices and dividingthe calculated vector y into a plurality of sub-vectors so as tocorrespond to the divided plurality of sub-upper triangular matrices;and detecting a lattice point corresponding to each of the dividedsub-vectors using the divided plurality of sub-upper triangularmatrices.

Another embodiment of the present invention provides a device fordetecting a transmission signal from a received signal in an MIMOsystem, the device including: a QR decomposition unit that obtains aunitary matrix Q and an upper triangular matrix R by performing an SQRDalgorithm with respect to a matrix B indicating a channel state; avector calculator that calculates a vector y by multiplying a transposematrix Q^(t) of the unitary matrix Q by the received signal Y; a dividerthat divides the upper triangular matrix R input from the QR decomposerinto a plurality of sub-upper triangular matrices and divides thecalculated vector y into a plurality of sub-vectors so as to correspondto the divided plurality of sub-upper triangular matrices; and adetector that detects a lattice point corresponding to each of thedivided sub-vectors using the divided plurality of sub-upper triangularmatrices input from the divider.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating the structure of a transmissionsignal detection device according to a first exemplary embodiment of thepresent invention.

FIG. 2 is a block diagram illustrating a detailed structure of thetransmission signal detection device according to the first exemplaryembodiment of the present invention.

FIG. 3 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a second exemplaryembodiment of the present invention.

FIG. 4 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a third exemplaryembodiment of the present invention.

FIG. 5 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a fourth exemplaryembodiment of the present invention.

FIG. 6 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a fifth exemplaryembodiment of the present invention.

FIG. 7 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a sixth exemplaryembodiment of the present invention.

FIG. 8 is a block diagram illustrating a detailed structure of atransmission signal detection device according to a seventh exemplaryembodiment of the present invention.

FIG. 9 is a flowchart illustrating a method of detecting a transmissionsignal, to which a division detection method is adopted, according tothe first exemplary embodiment of the present invention.

FIG. 10 is a flowchart illustrating a first example of step S107 shownin FIG. 9 in detail.

FIG. 11 is a flowchart illustrating an example of step S109 shown inFIG. 9 to which S107 shown in FIG. 10 is applied.

FIG. 12 is a flowchart illustrating a method of calculating alog-likelihood ratio by applying the flowcharts shown in FIGS. 10 and11.

FIGS. 13 and 14 are flowcharts illustrating steps S401 and S403 shown inFIG. 12 in detail.

FIG. 15 is a flowchart illustrating another example of step S109 shownin FIG. 9 by applying the flowcharts shown in FIGS. 10 and 11.

FIG. 16 is a flowchart illustrating a method of calculating thelog-likelihood ratio according to another example of step S109 byapplying the flowcharts shown in FIGS. 10 and 11.

FIG. 17 is a flowchart illustrating a second example of step S107 shownin FIG. 9 in detail.

FIG. 18 is a flowchart illustrating an example of step S109 shown inFIG. 9 to which S107 shown in FIG. 17 is applied.

FIG. 19 is a flowchart illustrating another example of step S109 towhich step S107 shown in FIG. 17 is applied.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Hereinafter, the present invention now will be described more fully withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown as those skilled in the art would realize. Asthose skilled in the art would realize, the described embodiments may bemodified in various different ways, all without departing from thespirit or scope of the present invention. Further, for more apparentdescription of the present invention with reference to the drawings,parts that have no relationship with the description are omitted andsimilar parts are represented by the same reference numerals through thespecification.

In addition, a part that includes a constituent element means that thepart may further include other constituent elements rather than only theconstituent element.

Further, the term “module” described in this specification means oneunit that processes a specific function or an operation and may beimplemented by hardware, software, or a combination of hardware andsoftware.

Hereinafter, a method and device for detecting a transmission signal towhich a division detection method is applied according to exemplaryembodiments of the present invention will be described in detail withreference to the accompanying drawings.

First, an exemplary embodiment of the present invention is applied to amultiple input multiple output (MIMO) system that includes multipletransmission/received signals. Here, the present invention is related toa division detection method and a device realizing the same that arecapable of assuming a transmission vector from a reception vector orreliability value of each bit included in a transmission vector so as toadjust the performance to be equal to or higher than BLAST (BellLaboratories Layered Space Time) and adjust an amount of calculation fordetection in accordance with a target performance. When the targetperformance is low, the amount of calculation decreases.

A system model to be used may be defined as follows.

In the MIMO system having M_(t) number of transmitting antennas andM_(r) number of receiving antennas and using a 2Q-QAM signalconstellation, a math model of Equation 1 is obtained so as to detectthe transmission signal.Y=BX+Z,Y=[Y ₁ . . . Y _(N)]^(t) ,X=[X ₁ . . . X _(M)]^(t) ,Z=[Z ₁ . . .Z _(N)]^(t)  [Equation 1]

Here, Y is a column vector that includes N number of signals known inthe receiving terminal, X is a column vector that includes M number ofcolumns as signals to obtain, and B is an N×M matrix assumed andcalculated in the receiving terminal. B is sometimes the same as achannel matrix, but is generally different from the channel matrix. Eachvalue of elements of B is represented by a complex number.

M and N may be the same or different from each other. Z is a vectorincluding N number of probability variables. Generally, an average of Zis a zero vector, and each of Z₁, Z₂, . . . , Z_(N) are independent fromeach other.

When Z_(i) (1≦i≦N) is in a Gaussian distribution, a value of X thatmakes a likelihood value with respect to the given Y and B be the sameas a value of X makes a distance between Y and BX the smallest.

When each element included in X is included in 2Q-QAM, all the capablelattice points are substituted into X so as to calculate a distancebetween Y and BX. In order to find a value of X that makes the distancebetween Y and BX the smallest, Equation 1 should be performed withrespect to 2MQ number of points. Therefore, when values of M and Q arelarge, the amount of calculation increases by geometric progression.

Accordingly, according to the exemplary embodiment of the presentinvention, when the values of M and Q are large, the performance may bedeteriorated as compared with the performance of the maximum likelihooddetection. However, even when the performance is deteriorated, theamount of calculation should be reduced by dividing and detecting thetransmission signal vector. Performance of the method of detecting eachof the divided signal vectors is similar to or the same as theperformance of the maximum likelihood detection. A method in which theamount of calculation is the smallest should be selected under the sameperformance.

In order to divide and detect the transmission signal vector X, thetransmission signal vector should be easily divided by modifyingEquation 1, and divided sub-transmission signal vectors should bedetected.

Next, the structure of the device for detecting a signal, which adoptsthe method of detecting the transmission signal based on above-describeddivision detection, will be described.

FIG. 1 is a block diagram illustrating the structure of a transmissionsignal detection device according to a first exemplary embodiment of thepresent invention.

Referring to FIG. 1, a transmission signal detection device according tothe division detection method includes a QR decomposer 100, a vectorcalculator 200, a divider 300, and a detector 400.

The QR decomposer 100 performs a sorted QR-decomposition (SQRD)algorithm to a matrix B that indicates a channel state so as to obtain aunitary matrix Q and an upper triangular matrix R.

At this time, the QR decomposer 100 applies SQRD or

$\begin{bmatrix}B \\{\sigma\; I_{M}}\end{bmatrix}\quad$to obtain

$\begin{bmatrix}B \\{\sigma\; I_{M}}\end{bmatrix}{\quad{= {QR}}}$where σ is the reciprocal of the square root of a signal-to-noise ratiomeasured in the receiving terminal and I_(M) is the identity matrix withthe size of the signal vector to be detected.

Otherwise, the QR decomposer 100 rearranges the columns of the matrix B,representing the channel state, in increasing order of the Euclideannorms of the columns and then applies QR dcomposition on the rearrangedmatrix B to obtain B=QR.

Further, the QR decomposer 100 rearranges the columns of the matrix B,representing the channel state, in increasing order of the Euclideannorms of the columns and then applies QR dcomposition on the matrix

$\begin{bmatrix}B \\{\sigma\; I_{M}}\end{bmatrix}\quad$where σ is the reciprocal of the square root of a signal-to-noise ratiomeasured in the receiving terminal and I_(M) is the identity matrix withthe size of the signal vector to be detected.

The vector calculator 200 calculates a vector y by multiplying atranspose matrix Q^(t) of the unitary matrix Q by the received signal Y.

The divider 300 divides an upper triangular matrix R input by the QRdecomposer 100 into a plurality of sub-upper triangular matrices anddivides the vector y input from the vector calculator 200 into aplurality of vectors so as to correspond to the divided plurality ofsub-upper triangular matrices.

The detector 400 detects the lattice point corresponding to each of thedivided sub-vectors by using the plurality of sub-upper triangularmatrices input from the divider 300.

FIG. 2 is a block diagram illustrating a detailed structure of a divider300 and a detector 400 according to the first exemplary embodiment ofthe present invention.

Referring to FIG. 2, the divider 300 includes a first sub-uppertriangular matrix division module 310 and a first vector division module320.

The first sub-upper triangular matrix division module 310 divides theupper triangular matrix R by a predetermined row i₀ determined on thebasis of SNR or the number of rows and obtains an (M−i₀)×(M−i₀)submatrix and an (i₀×M submatrix of the upper triangular matrix R. Thatis, the first sub-upper triangular matrix division module 310 obtains afirst sub-upper triangular matrix bR[i₀] that includes elements from an(i₀+1)-th column to an M-th column included from an (i₀+1)-th row to anM-th row of the upper triangular matrix R and a second sub-uppertriangular matrix uR[i₀] that includes elements from a first column toan i₀-th column included from a first row to an i₀-th row of the uppertriangular matrix R.

The first vector division module 320 divides the vector y into the firstsub-vector y_([1]) including elements from the (i₀+1)-th row to M-th rowand the second sub-vector y_([2]) including elements from a first row tothe i₀-th row so as to correspond to each of the first sub-uppertriangular matrix bR[i₀] and the second sub-upper triangular matrixuR[i₀].

The detector 400 includes a first lattice point detection module 410, afirst operation module 412, and a second lattice point detection module414.

The first lattice point detection module 410 detects a lattice point vin which the value of a product of the first sub-upper triangular matrixbR[i₀] and the lattice point v is the closest to the first sub-vectory_([1]) in distance.

The first operation module 412 calculates a transformational secondsub-vector y′_([2]) by eliminating a value of a product of the submatrixthat includes elements from the (i₀+1)-th row to the M-th row of thesecond sub-upper triangular matrix uR[i₀] and the lattice point v in thesecond sub-vector y_([2]).

The second lattice point detection module 414 detects a lattice point uat which the value of a product of the submatrix that includes elementsfrom the first row to the i₀-th row of the second sub-upper triangularmatrix uR[i₀] and the desired lattice point is the closest to the secondsub-vector y′_([2]) in distance.

FIG. 3 is a block diagram illustrating a detailed structure of alog-likelihood ratio calculator to which the structure shown in FIG. 2is applied according to a first exemplary embodiment of the presentinvention.

Referring to FIG. 3, the structure of the log-likelihood ratiocalculator includes a first log-likelihood ratio calculator 500 and asecond log-likelihood ratio calculator 600. Each log-likelihood ratio(LLR) corresponding to the transmission signal vector including elementsfrom the (i₀+1)-th row to M-th row and the transmission signal vectorincluding elements from the first row to the i₀-th row is calculated bya max-log map algorithm using the detected lattice point v and thelattice point u, respectively.

The first log-likelihood ratio calculator 500 calculates alog-likelihood ratio vector corresponding to the first sub-vectory_([1]) using the lattice point v and the max-log map algorithm. Moreparticular, the first log-likelihood ratio calculator 500 includes thefirst operation module 510 and the second operation module 520.

The first operation module 510 calculates a lattice point v(i,k) thatbecomes the closest to the first sub-vector y_([1]) in distance when thefirst sub-upper triangular matrix bR[i₀] is multiplied with a latticepoint of an M−i₀-th degree having a value obtained by inverting a k-thbit value at a bit string corresponding to an i-th signal (where1≦i≦M−i₀) of the lattice point v, as a bit value of a correspondingposition.

The second operation module 520 obtains a log-likelihood ratio LLR_(i+i)₀ _(,k) of the k-th bit of a bit string corresponding to an i+i₀-thsignal of the transmission signal vector using a difference between avalue of the product of the first sub-upper triangular matrix bR[i₀] andthe lattice point v(i,k) with respect to the first sub-vector y_([1]) indistance, and a value of product of the first sub-upper triangularmatrix bR[i₀] and the lattice point v with respect to the firstsub-vector y_([1]) in distance.

The second log-likelihood ratio calculator 600 calculates alog-likelihood ratio vector corresponding to the second sub-vectory_([2]) using the lattice point u and the max-log map algorithm. Moreparticularly, the second log-likelihood ratio calculator 600 includes afirst operation module 610 and a second operation module 620.

The first operation module 610 calculates a lattice point ū(i,k) thatbecomes the closest to the transformed second sub-vector y′_([2]) indistance when the second sub-upper triangular matrix uR[i₀] ismultiplied with a lattice point of a i₀-th degree having a valueobtained by inverting a k-th bit value at a bit string corresponding toan i-th signal (where 1≦i≦i₀) of the lattice point u, as a bit value ofa corresponding position.

The second operation module 620 obtains a log-likelihood ratio LLR_(i,k)of the k-th bit of the bit string corresponding to an i-th signal of thetransmission signal vector using a difference between a value of aproduct of the submatrix including elements from the first column to thei₀-th column of the second sub-upper triangular matrix uR[i₀] and thelattice point ū(i,k) with respect to the first sub-vector y′_([2]) indistance and a value of a product of the first sub-upper triangularmatrix uR[i₀] and the lattice point u with respect to the firstsub-vector y′_([2]) in distance.

FIG. 4 is a block diagram illustrating a detailed structure of a dividerand a detector according to the second exemplary embodiment of thepresent invention.

Referring to FIG. 4, since the structure of the divider 300 is the sameas shown in FIGS. 2 and 3, the description thereof will be omitted.

The detector 400 includes a third lattice point detection module 416, asecond operation module 418, and a fourth lattice point detection module420.

The third lattice point detection module 416 detects m number of latticepoints v[l] (where 1≦l≦m) in which a value of a product of the firstsub-upper triangular matrix bR[i₀] and the desired lattice points isless than a predetermined reference value with respect to the firstsub-vector y_([1]) in distance.

The second operation module 418 calculates, with respect to each l, thetransformed second sub-vector y′_([2])[l] by eliminating the value of aproduct of the lattice point v[l] and the submatrix that includeselements from an (i₀+1)-th column to an M-th column of the secondsub-upper triangular matrix uR[i₀] from the second sub-vector y_([2]).

The fourth lattice point detection module 420 detects a plurality oflattice points u[l][h] in which the value of a product of the submatrixthat includes elements from a first column to an i₀-th column of thesecond sub-upper triangular matrix uR[i₀] and the lattice points withrespect to the transformed second sub-upper triangular matrixy′_([2])[l] in distance is less than the predetermined reference value.

FIG. 5 is a block diagram illustrating a detailed structure of alog-likelihood ratio calculator to which the structure shown in FIG. 4is applied according to the second exemplary embodiment of the presentinvention.

Referring to FIG. 5, a third log-likelihood ratio calculator 700 thatcalculates the log-likelihood ratio using the lattice points output fromthe detector 400 calculates the log-likelihood ratio LLR_(i,k) of a k-thbit x_(i,k) of the bit string corresponding to the i-th signal by usinga sum d _(l)(u[l][h])+(v[l]) of each corresponding distance calculatedwith respect to a plurality of lattice points

$\begin{bmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{bmatrix}\quad$and the value α(i,k) to which a log is applied to the previousprobability ratio.

FIG. 6 is a block diagram illustrating a detailed structure of a dividerand a detector according to the third exemplary embodiment of thepresent invention.

Referring to FIG. 6, the structured of the divider 300 is the same asthe structure shown in FIGS. 2 to 5. Therefore, a detailed descriptionthereof will be omitted.

The detector 400 includes a fifth lattice point detection module 422, athird operation module 424, a sixth lattice point detection module 426,and a seventh lattice point detection module 428.

The fifth lattice point detection module 422 detects m number of latticepoints v[l] (where 1≦l≦m) in which the value of a product of the firstsub-upper triangular matrix bR[i₀] and the desired lattice points withrespect to the first sub-vector y_([1]) in distance is less than apredetermined reference value.

The third operation module 424 calculates, with respect to each l (where1≦l≦m), the transformed second sub-vector y′_([2])[l] by eliminating thevalue of a product of the lattice point v[l] and the submatrix thatincludes elements from the i₀+1-th column to the M-th column of thesecond sub-upper triangular matrix uR[i₀] from the second sub-vectory_([2]).

The sixth lattice point detection module 426 detects, with respect toeach l where 1≦l≦m), a plurality of lattice points u[l] in which thevalue of a product of the submatrix that includes elements from thefirst column to the i₀-th column of the second sub-upper triangularmatrix uR[i₀] and the desired lattice points is the closest to thetransformed second sub-upper triangular matrix y′_([2])[l] in distance.

The seventh lattice point detection module 428 receives distance valuesd(v[l]) and d _(i)(u[l]) corresponding to the detected plurality oflattice points v[l] and u[l] so as to select a lattice point

$\begin{bmatrix}{u\left\lfloor l_{0} \right\rfloor} \\{v\left\lbrack l_{0} \right\rbrack}\end{bmatrix}\quad$at which a value of d(v[l])+ d _(i)(u[l]) is minimized.

FIG. 7 is a block diagram illustrating a detailed structure of a dividerand a detector according to a fourth exemplary embodiment of the presentinvention.

Referring to FIG. 7, the divider 300 includes a second sub-uppertriangular matrix division module 330 and a second vector divisionmodule 340.

The second sub-upper triangular matrix division module 330 divides theupper triangular matrix R into a plurality of sub-upper triangularmatrices R[k] (where 0≦k≦a+1) according to a plurality of specific rowsdetermined by the SNR or the number of rows (i₀, i₁, . . . , i_(a),1≦i₀<i₁< . . . <i_(a)<M, where M is the entire number of rows of theupper triangular matrix R) as follows.

$\begin{matrix}{{{R\left\lbrack {a + 1} \right\rbrack}_{ij}:=R_{{({i_{a} + i})}{({i_{a} + j})}}},} & {{1 \leq i},{j \leq {M - i_{a}}}} \\{{{R\lbrack a\rbrack}_{ij}:=R_{{({i_{a - 1} + i})}{({i_{a - 1} + j})}}},} & {{1 \leq i \leq {i_{a} - i_{a - 1}}},{1 \leq j \leq {M - i_{a - 1}}}} \\\vdots & \; \\{{{R\lbrack k\rbrack}_{ij}:=R_{{({i_{k - 1} + i})}{({i_{k - 1} + j})}}},} & {{1 \leq i \leq {i_{k} - i_{k - 1}}},{1 \leq j \leq {M - i_{k - 1}}}} \\\vdots & \; \\{{{R\lbrack 1\rbrack}_{ij}:=R_{{({i_{0} + i})}{({i_{0} + j})}}},} & {{1 \leq i \leq {i_{1} - i_{0}}},{1 \leq j \leq {M - i_{0}}}} \\{{{R\lbrack 0\rbrack}_{ij}:=R_{ij}},} & {{1 \leq i \leq i_{0}},{1 \leq j \leq M}}\end{matrix}$

The second vector division module 340 divides the vector y into aplurality of sub-vectors y_([k]) (where 0≦k≦a+1) so as to correspond tothe plurality of sub-upper triangular matrices R[k] (where 0≦k≦a+1). An(a+2)-th sub-vector y_([0]) is a sub-vector that includes elements froma first row to an i₀-th row of the vector y and an (a+2-k)-th sub-vectory_([k]) is a sub-vector from an i_(k−1)+1-th row to an i_(k)-th row ofthe vector y (where 1≦k≦a). The first sub-vector y_([a+1]) divides thevector y into sub-vectors from the i_(a)-th row to the M-th row.

The detector 400 includes an eighth lattice point detection module 430,a fourth operation module 432, a fifth operation module 434, a sixthoperation module 436, a ninth lattice point detection module 438, and afirst output module 440.

The eighth lattice point detection module 430 calculates a lattice pointv(a+1) in which a value of a product of the sub-upper triangular matrixR[a+1] and a desired lattice point is the closest in distance from afirst sub-vector y_([a+1]).

The fourth operation module 432 sets i⁻¹=0 and substitutes a as aninitial value of k.

The fifth operation module 434 calculates a column vector

$w = \begin{bmatrix}{v\left( {k + 1} \right)} \\\vdots \\{v\left( {a + 1} \right)}\end{bmatrix}$in which the obtained vectors with respect to the given k, that is,column of vectors, are sequentially arranged from v(k+1) to v(a+1).

The sixth operation module 436 calculates an (a+2-k)-th transformedsub-vector y′_([k]) by eliminating a value of a product of the columnvector w and the submatrix that includes elements from an(i_(k)−i_(l−1)+1)-th column to an (M−i_(k−1))-th column of the sub-uppertriangular matrix R[k] from the (a+2-k)-th sub-vector y_([k]).

The ninth lattice point detection module 438 calculates a lattice pointv(k) that causes a value of a product of a desired lattice point and thesubmatrix that includes elements from a first column to an(i_(k)−i_(k−1))-th column of the sub-upper triangular matrix R[k] withrespect to the (a+2-k)-th transformed sub-vector y′_([k]) to be thesmallest in distance.

The first output module 440 substitutes k−1 to k. When k is equal to orlarger than 0, in order to obtain a column vector

$w = \begin{bmatrix}{v\left( {k + 1} \right)} \\\vdots \\{v\left( {a + 1} \right)}\end{bmatrix}$in which the column vectors from a v(k+1)-th column to a v(a+1)-thcolumn are sequentially arranged, the first output module 440 outputs acontrol signal to drive the fifth operation module 434. When k is −1,the first output module 440 outputs the lattice point

$\begin{bmatrix}{v(0)} \\{v(1)} \\\vdots \\{v\left( {a + 1} \right)}\end{bmatrix}.$

That is, the first output module 440 outputs the control signal to drivethe fifth operation module 434 until k becomes −1 so as to repeat theoperations performed by the fifth operation module 434, the sixthoperation module 436, and the ninth lattice point detection module 438.

FIG. 8 is a block diagram illustrating a detailed structure of a dividerand a detector according to a fifth exemplary embodiment of the presentinvention.

Referring to FIG. 8, since the structure of the divider 300 is the sameas shown in FIG. 7, a detailed description thereof will be omitted.

The detector 400 includes a seventh operation module 442, an eighthoperation module 444, a tenth lattice point detection module 446, and asecond output module 450.

The seventh operation module 442 calculates a corresponding distancevalue d(v) and a number of (n_(a+1)) lattice points v, in which a valueof a product of the sub-upper triangular matrix R[a+1] and the desiredlattice point with respect to the first sub-vector y[_(a+1]) in distanceis less than a predetermined reference value. At this time, a set ofn_(a+1) number of lattice points v is defined as Σ.

The eighth operation module 444 sets i⁻¹=0, and substitute a to k as aninitial value of k.

The tenth lattice point detection module 446 detects a plurality oflattice points u with respect to each lattice point v included in theset Σ. At this time, the sum d(u) of the value of a product of thesubmatrix that includes elements from an {(i_(k)−i_(k−1))+1}-th columnto an (M−i_(k−1))-th column of the sub-upper triangular matrix R[k] andthe lattice point v and the value of a product of the submatrix thatincludes elements from a first column to an (i_(k)−i_(k−1))-th column ofthe sub-upper triangular matrix R[k] and the lattice point u withrespect to the (a+2-k)th sub-vector y_([k]) in distance should be lessthan a predetermined reference value. At the same time, the tenthlattice point detection module 446 detects n_(k) number of latticepoints

$\quad\begin{bmatrix}u \\v\end{bmatrix}$in which a sum of a value of distance d(v) and a value of distance d(u)is less than the predetermined reference value.

A ninth operation module 448 designates a sum of the distance d(v) andthe distance d(u) to

$d\left( \begin{bmatrix}u \\v\end{bmatrix} \right)$and the set of n_(k) number of lattice points

$\quad\begin{bmatrix}u \\v\end{bmatrix}$as a symbol of the set ‘Σ’.

The second output module 450 substitutes k−1 to k. When k is equal to orlarger than 0, the second output module 450 outputs a control signal tocontrol to drive the tenth lattice point detection module 446 in orderto obtain a new Σ with respect to the changed k using a previous Σ. Whenk is −1, the second output module 450 outputs Σ which is the set of thestored lattice points.

Even though it is not shown in the drawings, a transmission signaldetection device according to another exemplary embodiment of thepresent invention has substantially the same structure as the structureshown in FIG. 1 and is implemented by applying a plurality of receivedsignals and a matrix that indicates channel states estimated withrespect to each of a plurality of received signals Y. The transmissionsignal detection device according to this exemplary embodiment of thepresent invention includes a QR decomposer, a vector calculator, adivider, and a detector. In this case, the transmission signal detectiondevice according to this exemplary embodiment of the present inventionis applied to a multi-step decoder as an example. At this time, repeateddescriptions will be omitted for each structure and only the relatedstructures will be described as follows.

The divider may include a first sub-upper triangular matrix divisionmodule and a first sub-vector division module.

The first sub-upper triangular matrix division module divides aplurality of upper triangular matrices R_({l}) (where 1≦l≦L) into afirst sub-upper triangular matrix bR_({l})[i₀] (where 1≦l≦L) which is an(M−i₀)×(M−i₀) matrix and a second sub-upper triangular matrixuR_({l})[i₀] (where 1≦l≦L) which is an (i₀×M) matrix based on apredetermined row i₀ determined on the basis of the SNR or the number ofrows.

The second sub-vector division module divides each of a plurality ofvectors y^({l}) (where 1≦l≦L) into a first sub-vector y_([1]) ^({l}) anda second sub-vector y_([2]) ^({l}) so as to correspond to each of thedivided first sub-upper triangular matrix bR_({l})[i₀] and the secondsub-upper triangular matrix uR_({l}[i) ₀].

At this time, the detector may include a first lattice point detectionmodule, a first operation module, and a second lattice point detectionmodule.

The first lattice point detection module detects a lattice point v inwhich a value of a product of the first sub-upper triangular matrixbR_({l})[i₀] and the lattice point with respect to the first sub-vectory_([1]) ^({l}) in distance is the closest for l (where 1≦l≦L).

The first operation module obtains the transformed second sub-vectory′_([2]) ^({l}) by eliminating the value of a product of the latticepoint v and the submatrix that includes elements from an (i₀+1)-thcolumn to the M-th column of the second sub-upper triangular matrixuR_({l}[i) ₀] from the second sub-vector y_([2]) ^({l}) (where 1≦1≦L).

The second lattice point detection module detects a lattice point u inwhich the value of product of the lattice point and the submatrix thatincludes elements from a first column to the i₀-th column of the secondsub-upper triangular matrix uR_({l})[i₀] (where 1≦l≦L) in distance isthe closest from the second sub-vector y′_([2]) ^({l}).

At this time, the first log-likelihood ratio calculator calculates thelog-likelihood ratio LLR_(i+i) ₀ _(,k) of a k-th bit of an (i+i₀)-th bitstring of the signal transmission vector corresponding to each of thevectors y^({l}) (where 1≦l≦L) and the log-likelihood ratio LLR_(i,k)^({l}) of a k-th bit of the bit string corresponding to an i-th signalusing each of the first sub-upper triangular matrix bR_({l})[i₀] (where1≦l≦L) and the second sub-upper triangular matrix uR_({l})[i₀] (where1≦l≦L). More specifically, a first operation module, a third latticepoint detection module, and a second operation module may be provided.

The first operation module may repeat calculation of the log-likelihoodratio LLR_(i+i) ₀ _(,k) ^({l}) of a k-th bit of an (i+i₀)-th bit stringof the signal transmission vector corresponding to each of the vectorsy^({l}) (where 1≦l≦L) using the first sub-upper triangular matrixbR_({l})[i₀].

The third lattice point detection module decodes a log-likelihood ratiovector LLR_(i+i) ₀ _(,k) ^({l}) (where 1≦l≦L) so as to detect thelattice point v^({1})=[v₁ ^({l}) . . . v_(M−i) ₀ ^({l})].

The second operation module calculates the log-likelihood ratioLLR_(i,k) ^({l}) of the k-th bit of the bit string corresponding to thei-th signal of the signal transmission vector corresponding to each ofthe vectors y^({l}) (where 1≦l≦L) using the lattice point v^({l})=[v₁^({l}) . . . v_(M−i) ₀ ^({1})] and the second sub-upper triangularmatrix uR_({l})[i₀].

On the other hand, the divider divides the upper triangular matrix Rinto a plurality of submatrices. The divider includes a second sub-uppertriangular matrix division module and a second sub-vector divisionmodule.

The second sub-upper triangular matrix division module divides aplurality of upper triangular matrices R_({l}) (where 1≦l≦L) into aplurality of sub-upper triangular matrices R_({l})[k] (where k is a, . .. , 1, 0) by applying predetermined rows (i₀, i₁, . . . , i_(a),1≦i₀<i₁< . . . <i_(a)<M) determined on the basis of the SNR or thenumber of rows.

The second sub-vector division module divides the vector y^({l}) into aplurality of sub-vectors y^({l})[k] (where k is a, . . . , 1, 0) so asto be corresponded to the plurality of sub-upper triangular matricesR_({l})[k] (where k is a, . . . , 1, 0).

At this time, the detector may include a first operation module and afirst detection module. First, the first operation module calculates atransformed sub-vector y′^({l})[k] which is transformed by eliminating adetected signal vector corresponding to a not-decreased k among aplurality of sub-vectors y^({l})[k] (where k is a, . . . , 1, 0), thatis, k decreases one by one from a+1 to reach 0.

Hereinafter, a method of detecting a signal to which the above-describeddivision detection method is applied will be described on the basis ofthe structure of the transmission signal detection device.

FIG. 9 is a flowchart illustrating a method of detecting a transmissionsignal, to which a division detection method according to the exemplaryembodiment of the present invention is adopted.

Referring to FIG. 9, in the method of detecting a transmission signal,the matrix B indicating the channel state is converted into a realnumber matrix A (step S101). If the matrix B includes real numberelements, matrix A is set to be equal to the matrix B. Otherwise, thematrix A is set as

$A = {\begin{bmatrix}{{Re}\left\{ B \right\}} & {{- {Im}}\left\{ B \right\}} \\{{Im}\left\{ B \right\}} & {{Re}\left\{ B \right\}}\end{bmatrix}.}$Here, the number of columns in the matrix A is set to M. When eachsignal of the transmission signal vector is divided into a real part andan imaginary part, the number of bits included in the bit stringcorresponding to the real part (or the imaginary part) in the signalconstellation is set to Q.

The SQRD algorithm is applied to the real number matrix A converted instep S101 so as to obtain the unitary matrix Q and upper triangularmatrix R (step S103).

Here, when the SQRD algorithm is performed for the matrix A, A is set tobe equal to QR. When the SQRD algorithm is performed for

$\begin{bmatrix}A \\{\sigma\; I_{M}}\end{bmatrix},\begin{bmatrix}A \\{\sigma\; I_{M}}\end{bmatrix}$is set to be equal to QR. Here, σ indicates the reciprocal of the squareroot of a signal-to-noise ratio and I_(M) indicates an M by M identitymatrix. Q indicates a unitary matrix and R indicates an upper triangularmatrix. At this time, the amount of calculation thereafter may bereduced by using

$\begin{bmatrix}A \\{\sigma\; I_{M}}\end{bmatrix}.$

At this time, the transmission signal corresponding to the column numberof the matrix in which the SQRD algorithm is not performed and thetransmission signal corresponding to a column number of R are differentfrom each other. Therefore, in the transmission signal, the sorted ordershould be stored.

The SQRD algorithm may be used with a PSA (past-sorting algorithm). Thelarger the column number, the larger the SNR in the R corresponding tothe number.

In the SQRD algorithm, the sorting and the QR-decomposition aresimultaneously performed. Instead of the SQRD algorithm, each of thecolumns included in the matrix A are sequentially arranged in the orderof the Euclidean norm of each column vector. Further, the unitary matrixand the upper triangular matrix obtained by QR decomposition withrespect to the arranged matrix may be set to Q and R, respectively.

Here, the QR decomposition may be implemented by following threeexemplary embodiments.

According to the first exemplary embodiment, the sorted QR decomposition(SQRD) is applied on

$\quad\begin{bmatrix}A \\{\sigma\; I_{M}}\end{bmatrix}$where σ is the reciprocal of the square root of a signal-to-noise ratiomeasured in the receiving terminal and I_(M) is the identity matrix withthe size of the signal vector to be detected.

According to the second exemplary embodiment, the QR decomposition isapplied on the matrix A after the columns of the matrix A are rearrangedin increasing order of the Euclidean norm of each column vector.

According to the third exemplary embodiment, the columns of the matrixA, representing the channel state, are rearranged in increasing order ofthe Euclidean norm of each column vector and then QR decomposition isapplied on

$\quad\begin{bmatrix}A \\{\sigma\; I_{M}}\end{bmatrix}$where σ is the reciprocal of the square root of a signal-to-noise ratiomeasured in the receiving terminal and I_(M) is the identity matrix withthe size of the signal vector to be detected.

Next, the vector y is obtained by multiplying a transpose matrix Q^(t)of the unitary matrix Q by the received signal Y (step S105).

Equation 2 will show y that satisfies following equation, that is,

$y = {{Q^{t}\begin{bmatrix}{{Re}\left\{ Y \right\}} \\{{Im}\left\{ Y \right\}}\end{bmatrix}}.}$

$\begin{matrix}{{y = {{R\begin{bmatrix}{{Re}\left\{ X \right\}} \\{{Im}\left\{ X \right\}}\end{bmatrix}} + \eta}},{\eta = {Q^{t}\begin{bmatrix}{{Re}\left\{ Z \right\}} \\{{Im}\left\{ Z \right\}}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

At this time, η and

$\quad\begin{bmatrix}{{Re}\left\{ Z \right\}} \\{{Im}\left\{ Z \right\}}\end{bmatrix}$have the same probability distribution and Equation 2 is equivalent toEquation 1.

Hereinafter, it is represented as y=[y₁ y₂ . . . y_(M)]^(t),

${x = {\begin{bmatrix}{{Re}\left\{ X \right\}} \\{{Im}\left\{ X \right\}}\end{bmatrix} = \left\lbrack {x_{1}\mspace{14mu} x_{2}\mspace{14mu}\ldots\mspace{14mu} x_{M}} \right\rbrack^{t}}},$and η=[η₁ η₂ . . . η_(M)]^(t).

Next, the upper triangular matrix R is divided into a plurality ofsub-upper triangular matrices on the basis of a predetermined row i₀determined on the basis of the SNR or the number of rows, and then thevector y is divided so as to correspond to the divided sub-uppertriangular matrices (step S107).

Next, the lattice point corresponding to the corresponding sub-vector isdetected using the divided plurality of sub-upper triangular matrices(step S109).

FIG. 10 is a flowchart illustrating a first example of step S107 shownin FIG. 9, in detail.

Referring to FIG. 10, first, the predetermined row i₀ is determined onthe basis of the SNR or the number of rows (step S201).

Next, the upper triangular matrix is divided into the first sub-uppertriangular matrix bR[i₀] which is the (M−i₀)×(M−i₀) matrix and thesecond sub-upper triangular matrix uR[i₀] which is the (i₀×M matrix onthe basis of the predetermined row i₀ (step S203).

At this time, the first sub-upper triangular matrix bR[i₀] is the(M−i₀)×(M−i₀) matrix having column vectors equal to or larger than the(i₀+1)-th column among the matrix having row vectors from the (i₀+1)-throw in which one is increased from the predetermined row i₀ to the lastM-th row of the upper triangular matrix R. The second sub-uppertriangular matrix uR[i₀] is the (i₀×M) matrix having the row vectorsfrom the first row to the ( )-th row of the upper triangular matrix R.

At this time, the first sub-upper triangular matrix and the secondsub-upper triangular matrix may be represented by Equation 3.bR[i ₀]_(ij) :=R _((i) ₀ _(+i)(i) ₀ _(+j)),1≦i,j≦M−i ₀uR[i ₀]_(ij) :=R _(ij),1≦i≦i ₀,1≦j≦M  [Equation 3]

Next, the vector y is divided into the first sub-vector y_([1]) and thesecond sub-vector y_([2]) so as to correspond to the first sub-uppertriangular matrix bR[i₀] and the second sub-upper triangular matrixuR[i₀] (step S205).

FIG. 11 is a flowchart illustrating a first example of step S109 shownin FIG. 9, in detail, and FIG. 11 is a flowchart illustrating a methodof detecting the lattice point by applying step S107 shown in FIGS. 9and 10.

Referring to FIG. 11, the lattice point may be detected by using thefollowing Equation 4.[Equation 4][y _(i) ₀ ₊₁ . . . y _(M)]^(t) =bR[i ₀ ][x _(i) ₀ ₊₁ . . . x_(M)]^(t)+[η_(i) ₀ ₊₁ . . . η_(M)]^(t)  (1)[y ₁ . . . y _(i) ₀ ]^(t) =uR[i ₀ ]x+[η ₁ . . . η_(i) ₀ ]^(t)  (2)

Here, [y_(i) ₀ ₊₁ . . . y_(M)]^(t) of (1) indicates the first sub-vectory_([1]) and [y₁ . . . y_(i) ₀ ]^(t) corresponds to the second sub-vectory_([2]).

The lattice point v in which the value of product of the first sub-uppertriangular matrix bR[i₀] and the desired lattice point v is the closestto the first sub-vector y_([1]) in distance is then detected (stepS301).

That is, [x_(i) ₀ ₊₁ . . . x_(M)]^(t) is obtained by (1) of Equation 4.At this time, η_(i) ₀ ₊₁, . . . , η_(M) indicates Gaussian noisesindependent from each other. Further, [x_(i) ₀ ₊₁ . . . x_(M)]^(t) existin an (M−i₀) dimensional space D₁ in which each coordinate is one of2^(Q) number of integral numbers.

Among the lattice points included in the space D₁, a point having thesmallest value is obtained by using following Equation 5.∥[y _(i) ₀ ₊₁ . . . y _(M)]^(t) −bR[i ₀ ][x _(i) ₀ ₊₁ . . . x _(M])^(t)∥²  [Equation 5]

The lattice point obtained by operating Equation 5 is represented asv=[v₁ . . . v_(M−i) _(o) ]^(t).

Next, the transformed second sub-vector y′_([2]) is obtained byeliminating the value of a product of the lattice point v and thesubmatrix that includes elements from the (i₀+1)-th column to the M-thcolumn of the second sub-upper triangular matrix uR[i₀] from the secondsub-vector y_([2]) (step S303).

That is, in (2) of Equation 4, v is substituted to [x_(i) ₀ ₊₁ . . .x_(M)], that is, x_(i) ₀ _(+i)=v_(i) (where 1≦i≦M−i₀) is set. And then,

$y_{j}^{\prime} = {y_{j} - {\sum\limits_{1 \leq i \leq {M - i_{0}}}{{{uR}\left\lbrack i_{0} \right\rbrack}_{j{({i_{0} + i})}}v_{i}}}}$for every j (where 1≦j≦i₀) is calculated. (Here, [y′₁ . . . y′_(i) ₀]^(t) is referred to as the transformed second sub-vector y′_([2]).)

Next, the lattice point u in which the value of a product of the latticepoint u and the submatrix that includes elements from the first columnto the i₀-th column of the second sub-upper triangular matrix uR[i₀] isthe closest to the transformed second sub-vector y′_([2]) in distance isdetected (step S305).

That is, the following Equation 6 is used.[y ₁ ^(t) . . . y _(i) ₀ ^(t)]^(t) =uR[i ₀](1:i ₀)[x ₁ . . . x _(i) ₀]^(t)+[η₁ . . . η_(i) ₀ ]^(t)  [Equation 6]

Here, uR[i₀](1:i₀) indicates the submatrix that includes elements fromthe first column to the i₀-th column.

At this time, [x₁ . . . x_(i) ₀ ]^(t) exists in an i₀-dimensional spaceD₂ at which the coordinate is one of 2^(Q) number of integral numbers.

Among the lattice points included in the space D₂, [x₁ . . . x_(i) ₀ ]causing the result of Equation 7 to be the smallest value is obtained byusing Equation 6.∥[y ₁ ^(t) . . . y _(i) ₀ ^(t)]^(t) −uR[i ₀](1:i ₀)[x ₁ . . . x _(i) ₀]^(t)∥²  [Equation 7]

[x₁ . . . x_(i) ₀ ] obtained by operating Equation 7 is output as thelattice point u=[u₁ . . . u_(i) ₀ ]^(t).

Finally,

$\overset{\Cap}{x} = \begin{bmatrix}u \\v\end{bmatrix}$is output as the transmission signal vector.

At this time, each of coordinates included in lattice points u and vshould correspond to the signal constellation mapping on signaltransmission and the result of the conversion equation thereof. In orderto obtain the lattice points u and v, a plurality of algorithms, such asa sphere decoding algorithm, a near ML technology such as the QRM-MLD,and a sequential interference elimination algorithm may be selected.

In order to check the decrement of the amount of calculation, it isassumed that a full search is performed in the spaces D₁ and D₂ whendetecting the lattice points v and u. In order to obtain {circumflexover (X)}, the distance of 2^(Q(M−i) ⁰ ⁾+2^(Qi) ⁰ number of points arecalculated. As the degree of the lattice points v and u is reduced, theamount of calculation necessary to calculate the distance is reduced.

FIG. 12 is a flowchart illustrating a method of calculating thelog-likelihood ratio by applying the flowchart shown in FIG. 10 and FIG.11.

Referring to FIG. 12, the log-likelihood ratio is calculated by thefollowing method. First, the log-likelihood ratio LLR corresponding tothe first sub-vector y_([1]) is obtained using the max-log map algorithmand the lattice point v obtained in FIG. 11 (step S401). Second, thelog-likelihood ratio (LLR) corresponding to the second sub-vectory_([2]) is obtained using the lattice point u and the max-log mapalgorithm obtained (step S403).

Specifically, in step S401, the log-likelihood ratio LLR_(i+i) ₀ _(,k)vector corresponding to ([x_(i) ₀ ₊₁ . . . x_(M)]^(t)) is obtained byusing the max-log map algorithm in (1) of Equation 4 with respect to[x_(i) ₀ ₊₁ . . . x_(M)]^(t).

Further, in step S403, the log-likelihood ratio LLR_(i,k) vectorcorresponding to [x₁ . . . x_(i) ₀ ]^(t) is calculated by substitutingthe lattice point v to [x_(i) ₀ ₊₁ . . . x_(M)] in (2) of Equation 4,that is, setting x_(i) ₀ _(+i)=v_(i) (where 1≦i≦M−i₀) and calculating

$y_{j}^{\prime} = {y_{j} - {\sum\limits_{1 \leq i \leq {M - i_{0}}}{{{uR}\left\lbrack i_{0} \right\rbrack}_{j{({i_{0} + i})}}v_{i}}}}$for every j (where 1≦j≦i₀).

FIGS. 13 and 14 are flowcharts illustrating steps S401 and S403 shown inFIG. 12 in detail.

FIG. 13 shows step S401 in detail. Referring to FIG. 13, a value of thek-th bit of the bit string corresponding to the i-th signal (where1≦i≦M−i₀) of the lattice point v is inverted (step S501). That is, ifthe value of the bit of the corresponding position is 0, it is changedto 1, and if the value of the bit of the corresponding position is 1, itis changed to 0.

In step S401, the lattice point v(i,k) in which the value of a productof the lattice point and the first sub-upper triangular matrix bR[i₀]with respect to the first sub-vector y_([1]) is the closest in distanceis obtained among the (M−i₀)-degree lattice points having the invertedbit value as the bit value of the k-th bit of the bit stringcorresponding to the i-th signal (step S503).

Next, the log-likelihood ratio (LLR_(i+i) ₀ _(,k)) of the k-th bit ofthe bit string corresponding to the (i+i₀)-th signal of the signaltransmission vector corresponding to the vector y is obtained by usingthe difference between the corresponding value of distance of thelattice point v(i,k) obtained in step S503 and the value of the productof the first sub-upper triangular matrix bR[i₀] and the lattice point vwith respect to the first sub-vector y_([1]) (step S505).

That is, the value of LLR of the k-th bit of the bit stringcorresponding to the (i+i₀)-th signal of the signal transmission vectormay be represented by (LLR_(i+i) ₀ _(,k)) as in the following Equation8.

$\begin{matrix}{{LLR}_{{i + i_{0}},k} = {\left( {- 1} \right)^{v_{i,k}}\frac{\begin{matrix}{{{\left\lbrack {y_{i_{0} + 1}\mspace{14mu}\ldots\mspace{14mu} y_{M}} \right\rbrack^{t} - {{{bR}\left\lbrack i_{0} \right\rbrack}{\overset{\_}{v}\left( {i,k} \right)}}}}^{2} -} \\{{\left\lbrack {y_{i_{0} + 1}\mspace{14mu}\ldots\mspace{14mu} y_{M}} \right\rbrack^{t} - {{{bR}\left\lbrack i_{0} \right\rbrack}v}}}^{2}\end{matrix}}{2\sigma^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

FIG. 14 shows step S403. Referring to FIG. 14, a value of the k-th bitof the bit string corresponding to the i-th signal (where 1≦i≦i₀) of thelattice point u is inverted with respect to the k-th bit of the bitstring of the i-th signal of the transmission vector (step S601).

Next, among the i₀-degree lattice points having the inverted bit valueas the k-th bit value of the bit string of the i-th signal, the latticepoint ū(i,k) in which the value of a product of the lattice point andthe submatrix that includes elements from the first column to the i₀-thcolumn of the second sub-upper triangular matrix uR[i₀] is the closestto the transformed second sub-vector y′_([2]) in distance is obtained(step S603).

Next, the log-likelihood ratio LLR_(i,k) of the k-th bit of the bitstring corresponding to the i-th signal of the signal transmissionvector corresponding to the vector y is calculated by using a differencebetween a value of a product of a value of a corresponding distance ofthe lattice point ū(i,k) obtained in step S603, that is, the submatrixthat includes elements from the first column to the i₀-th column of thesecond sub-upper triangular matrix uR[i₀], and the lattice point ū(i,k)with respect to the transformed second sub-vector y′_([2]) in distance,and a value of a product of the submatrix that includes elements fromthe first column to the i₀-th column of the second sub-upper triangularmatrix uR[i₀] and the lattice point u with respect to the transformedsecond sub-vector y′_([2]) in distance (step S605).

That is, the log-likelihood ratio LLR_(i,k) of the k-th bit of the bitstring corresponding to the i-th signal using the lattice point ū(i,k)obtained in step S603 may be calculated using the following Equation 9.

$\begin{matrix}{{LLR}_{i,k} = {\left( {- 1} \right)^{u_{i,k}}\frac{\begin{matrix}{{{\left\lbrack {y_{1}^{\prime}\mspace{14mu}\ldots\mspace{14mu} y_{i_{0}}^{\prime}} \right\rbrack^{t} - {{{uR}\left\lbrack i_{0} \right\rbrack}\left( {1:i_{0}} \right){\overset{\_}{u}\left( {i,k} \right)}}}}^{2} -} \\{{\left\lbrack {y_{1}^{\prime}\mspace{14mu}\ldots\mspace{14mu} y_{i_{0}}^{\prime}} \right\rbrack^{t} - {{{uR}\left\lbrack i_{0} \right\rbrack}\left( {1:i_{0}} \right)u}}}^{2}\end{matrix}}{2\sigma^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Next, a hard decision and a soft decision may be determined bytransforming the method of detection of a signal shown in FIG. 9.

FIG. 15 is a flowchart illustrating another example of step S109 shownin FIG. 9 by applying the flowcharts shown in FIGS. 10 and 11.

Referring to FIG. 15, a plurality of (m number of) lattice points v[l]in which the value of a product of the first sub-upper triangular matrixbR[i₀] and the lattice point v[l] to be detected is equal to or lessthan the value of a distance of a predetermined reference value withrespect to the first sub-vector y_([1]) is detected (step S701).

The plurality of lattice points v[l] that are close to the matrix [y_(i)₀ ₊₁ . . . y_(M)]^(t) corresponding to the first sub-upper triangularmatrix bR[i₀] are detected. That is, [x_(i) ₀ ₊₁ . . . x_(M)]^(t) isdetected using (1) of Equation 4. Particularly, m number of latticepoints including a point that has the smallest value of ∥[y_(i) ₀ ₊₁ . .. y_(M)]^(t)−bR[i₀][x_(i) ₀ ₊₁ . . . x_(M)]^(t)∥² and a point that hasthe value immediately larger than the smallest value of ∥[y_(i) ₀ ₊₁ . .. y_(M)]^(t)−bR[i₀][x_(i) ₀ ₊₁ . . . x_(M)]^(t)∥² are obtained. Here, mindicates a predetermined natural number that is set beforehand.Therefore, the obtained m number of lattice points is represented asv[l]=[v[l]₁ . . . v[l]_(M−i) ₀ ]^(t), 1≦l≦m.

Further, {v[1], v[2], . . . , v[m]} is referred to as the Λ and thevalues obtained from d(v[l]):=∥[y_(i) ₀ ₊₁ . . . y_(M)]^(t)−bR[i₀]v[l]∥²are stored.

Next, the transformed second sub-vector y′_([2])[l] is obtained byeliminating the value of the product of the lattice points v[l] and thesubmatrix that includes elements from the (i₀+1)-th column to the M-thcolumn of the second sub-upper triangular matrix uR[i₀] from the secondsub-vector y_([2]) (step S703).

The points of Λ are substituted to [x+_(i) ₀ ₊₁ . . . x_(M)] in (2) ofEquation 4. It is assumed that x_(i) ₀ ₊₁=v[l]_(t), 1≦i≦M−i₀ (wherev[l]εΛ, 1≦l≦m) and the form

${y_{j}^{\prime}\lbrack l\rbrack} = {y_{j} - {\sum\limits_{1 \leq i \leq {M - i_{0}}}{{{uR}\left\lbrack i_{0} \right\rbrack}_{j{({i_{0} + i})}}{v\lbrack l\rbrack}_{i}}}}$are calculated with respect to j (where 1≦j≦i₀). It can be arranged asin the following Equation 10.[y′ ₁ [l] . . . y′ _(i) ₀ [l]] ^(t) =uR[i ₀](1:i ₀)[x ₁ . . . x _(i) ₀]^(t)+[η₁ . . . η_(i) ₀ ]^(t)  [Equation 10]

Next, with respect to l (where 1≦l≦m), lattice points u[l] in which thevalue of a product of the submatrix that includes elements from thefirst column to the i₀-th column of the second sub-upper triangularmatrix uR[i₀] and the lattice point u[l] has the smallest value ofdistance with respect to the transformed second sub-vector y′_([2])[l]are detected (step S705).

That is, with respect to l (where 1≦l≦m) a smallest point obtained fromthe form of d ₁([x₁ . . . x_(i) ₀ ]^(t))=∥[y′₁[l] . . . y′_(i) ₀[l]]^(t)−uR[i₀](1:i₀)[x₁ . . . x_(i) ₀ ]^(t)∥² is calculated usingEquation 10 and the calculated smallest point is referred to as u[l].

Next, a lattice point

$\left\lbrack \left. \quad\begin{matrix}{u\left\lbrack l_{0} \right\rbrack} \\{v\left\lbrack l_{0} \right\rbrack}\end{matrix} \right\rbrack \right.$in which the sum of the corresponding value of distance d(v[l])+ d₁(u[l]) for each of the lattice points v and u with respect to each of aplurality of lattice points

$\left\lbrack \left. \quad\begin{matrix}{u\lbrack l\rbrack} \\{v\lbrack l\rbrack}\end{matrix} \right\rbrack \right.$detected by repeating step S703 and step S705 for the plurality oflattice point v[l] detected in step S701 is minimized is selected (stepS707).

That is, the form d(v[l])+ d ₁(u[l]) (where 1≦l≦m) is compared and thelattice point in which the value of d(v[l])+ d ₁(u[l]) is smallest isselected to output

$\overset{\Cap}{x} = \begin{bmatrix}{u\left\lbrack l_{0} \right\rbrack} \\{v\left\lbrack l_{0} \right\rbrack}\end{bmatrix}$as the signal transmission vector with respect to the vector.

FIG. 16 is a flowchart illustrating a method of calculating thelog-likelihood ratio according to another example of step S109 byapplying the flowcharts shown in FIGS. 10 and 11.

Referring to FIG. 16, the plurality of (m number of) lattice points v[l]in which a value of a product of the first sub-upper triangular matrixbR[i₀] and the desired lattice point with respect to the firstsub-vector y_([1]) in distance is equal to or less than thepredetermined reference value are detected (step S801).

That is, among the lattice points included in the space D₁, the m numberof points each having a small value of d([x_(i) ₀ ₊₁ . . .x_(M)])=∥[y_(i) ₀ ₊₁ . . . y_(M)]^(t)−bR[i₀][x_(i) ₀ ₊₁ . . .x_(M)]^(t)∥² are determined and stored on the basis of the form (1) ofEquation 4. The set of the obtained lattice points is indicated by asymbol Λ. Λ includes the lattice point having the smallest value of d(•)and the other m−1 number of lattice points are points until the m-thpoint other than the smallest point when sequentially arranging thelattice points calculated to search the lattice point having thesmallest value of d(•).

The points included in Λ, that is, the values corresponding to {v[1],v[2], . . . , v[m]}, are stored. Further, the points included in Λ aredefined as v[l] where 1≦l≦m.

Next, the transformed second sub-vector y′_([2])[l] is obtained byeliminating the value of a product of the lattice points v[l] and thesubmatrices from the (i₀+1)-th column to the M-th column of the secondsub-upper triangular matrix uR[i₀] from the second sub-vector y_([2])(step S803).

The points of Λ are substituted to [x_(i) ₀ ₊₁ . . . x_(M)] in the form(2) of Equation 4. That is, it is assumed that x_(i) ₀ ₊₁=v[l]_(i),1≦i≦M−i₀ (where v[l]εΛ, 1≦l≦m), and the form

${y_{j}^{\prime}\lbrack l\rbrack} = {y_{j} - {\sum\limits_{1 \leq i \leq {M - i_{0}}}{{{uR}\left\lbrack i_{0} \right\rbrack}_{j{({i_{0} + i})}}{v\lbrack l\rbrack}_{i}}}}$is calculated with respect to j (where 1≦j≦i₀).

Next, the plurality of lattice points u[l][h] in which the value of aproduct of the submatrix that includes elements from the first column tothe i₀-th column of the second sub-upper triangular matrix uR[i₀] andthe lattice point with respect to the transformed second sub-vectory′_([2])[l] in distance is equal to or smaller than the predeterminedreference value are detected (step S805).

That is, with respect to each l (where 1≦l≦m), n₁ number of latticepoints in which the distance value corresponds to the predeterminedreference value are detected with reference to the following Equation11. The value of n₁ with respect to l is a predetermined natural number.The n₁ number of points are represented as Λ₁. Λ₁ includes the pointhaving the smallest value of d ₁(•), and the other n₁−1 number of pointsare points until the n₁-th point other than the smallest point whensequentially arranging the points calculated to search the point havingthe smallest value of d ₁(•).

The values of d ₁(•) with respect to the points included in the Λ₁ arestored.d ₁([x ₁ . . . x _(i) ₀ ]^(t))=∥[y ₁ ^(t) [l] . . . y _(i) ₀ ′[l]] ^(t)−uR[i ₀](1:i ₀)[x ₁ . . . x _(i) ₀ ]^(t)∥²  [Equation 11]

Here, each coordinate of [x₁ . . . x_(i) ₀ ]^(t) is one of 2^(Q) numberof integral numbers, and each exists in the i₀-dimensional space D₂.

Next, it is calculated from the lattice point in which the result of

${{f\begin{pmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{pmatrix}} = {{{\overset{\_}{d}}_{l}\left( {{u\lbrack l\rbrack}\lbrack h\rbrack} \right)} + {d\left( {v\lbrack l\rbrack} \right)}}},\mspace{14mu}{{{u\lbrack l\rbrack}\lbrack h\rbrack} \in \Lambda_{l}}$becomes the smallest value to the lattice point in which the result of

${{f\begin{pmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{pmatrix}} = {{{\overset{\_}{d}}_{l}\left( {{u\lbrack l\rbrack}\lbrack h\rbrack} \right)} + {d\left( {v\lbrack l\rbrack} \right)}}},\mspace{14mu}{{{u\lbrack l\rbrack}\lbrack h\rbrack} \in \Lambda_{l}}$becomes the k-th smallest value, and then the set of those latticepoints

$S = \begin{bmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{bmatrix}$is calculated (step S807). That is, on the basis of Λ, Λ₁, . . . , Λ_(m)obtained in step S805, the numerical formula f(u,v[l])= d ₁(u)+d(v[l])is calculated with respect to l (1≦l≦m) for each uεΛ₁. The pointscorresponding from the smallest f(•) value to the k-th smallest f(•)value are stored. The symbol K indicates the natural numberpredetermined by considering the size of capable memory or the amount ofcalculation. The set of above-described obtained k number of points isset as S.

Next, the log-likelihood ratio LLR_(i,k) of the k-th bit x_(i,k) of thebit string corresponding to the i-th signal is calculated using the sumof each corresponding distances

$\left( {{f\begin{pmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{pmatrix}} = {{{\overset{\_}{d}}_{l}\left( {{u\lbrack l\rbrack}\lbrack h\rbrack} \right)} + {d\left( {v\lbrack l\rbrack} \right)}}} \right)$calculated with respect to the plurality of lattice points

$x = \begin{bmatrix}{{u\lbrack l\rbrack}\lbrack h\rbrack} \\{v\lbrack l\rbrack}\end{bmatrix}$and the value α(i,k) to which the log is applied to the previousprobability ratio of each bit (step S809).

That is, when calculating the LLR for the signal to be detected in asignal repeating receiver, if it is assumed that the k-th bit of the bitstring corresponding to the i-th signal of the transmission signalvector is denoted as x_(i,k), the LLR value of the x_(i,k) is denoted asLLR_(i,k), and the value to which the log is applied to the previousprobability ratio of the corresponding bit to be input for calculatingthe LLR is denoted as α(i,k), the LLR of the corresponding bit may becalculated by using following Equation. 12.

$\begin{matrix}{{LLR}_{i,k} \approx {{\alpha\left( {i,k} \right)} - {\frac{1}{2}{\min\limits_{{x \in S},{x_{i,k} = 0}}\left( {\frac{f(x)}{\sigma^{2}} - {\sum\limits_{{({j,s})} \neq {({i,k})}}{{\alpha\left( {j,s} \right)}\left( {- 1} \right)^{x_{j,s}}}}} \right)}} + {\frac{1}{2}{\min\limits_{{x \in S},{x_{i,k} = 1}}\left( {\frac{f(x)}{\sigma^{2}} - {\sum\limits_{{({j,s})} \neq {({i,k})}}{{\alpha\left( {j,s} \right)}\left( {- 1} \right)^{x_{j,s}}}}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

On the other hand, when detecting a signal by dividing Equation 2,Equation 2 may be divided by more than three detection formulas when thenumber of received signal strings and the number of transmission signalstrings are large as well as by dividing Equation 2 by two as inEquation 3. At this time, the method of dividing Equation 2 is the sameas the method of configuring Equation 3 and Equation 4. A specific rowthat divides Equation 2 may be determined by considering a signalstrength distribution of each column of the upper triangular matrix R ofEquation 2. If the signal strength distribution of each column is notconsidered in the upper triangular matrix R, each of the dividedrelations has the same number or similar number of variables.

FIG. 17 is a flowchart illustrating a second example of step S107 shownin FIG. 9 in detail.

Referring to FIG. 17, in the upper triangular matrix R, a plurality ofpredetermined rows i₀, i₁, . . . , i_(a) (where 1≦i₀<i₁< . . . <i_(a)<M,and the symbol M indicates the entire number of rows of the uppertriangular matrix R) determined on the basis of the SNR or the number ofrows are set (step S901).

Next, the upper triangular matrix R is divided into a plurality ofsub-upper triangular matrices R[k], 0≦k≦a+1 on the basis of theplurality of predetermined rows set in step S901 (step S903).

That is, when the number of rows of the upper triangular matrix R isassumed as M, the upper triangular matrix R is divided as Equation 13with respect to the (a+1) number of natural numbers i₀, i₁, . . . ,i_(a) (where 1≦i₀<i₁< . . . <i_(a)<M)

$\begin{matrix}{{{{R\left\lbrack {a + 1} \right\rbrack}_{ij}:=R_{{({i_{a} + i})}{({i_{a} + j})}}},{1 \leq i},{j \leq {M - i_{a}}}}{{{R\lbrack a\rbrack}_{ij}:=R_{{({i_{a - 1} + i})}{({i_{a - 1} + j})}}},{1 \leq i \leq {i_{a} - i_{a - 1}}},{1 \leq j \leq {M - i_{a - 1}}}}\vdots{{{R\lbrack k\rbrack}_{ij}:=R_{{({i_{k - 1} + i})}{({i_{k - 1} + j})}}},{1 \leq i \leq {i_{k} - i_{k - 1}}},{1 \leq j \leq {M - i_{k - 1}}}}\vdots{{{R\lbrack 1\rbrack}_{ij}:=R_{{({i_{0} + i})}{({i_{0} + j})}}},{1 \leq i \leq {i_{1} - i_{0}}},{1 \leq j \leq {M - i_{0}}}}{{{R\lbrack 0\rbrack}_{ij}:=R_{ij}},{1 \leq i \leq i_{0}},{1 \leq j \leq M}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

The vector y is divided into a plurality of sub-vectors y_([k]) (where0≦k≦a+1) so as to correspond to the plurality of sub-upper triangularmatrices R[k], 0≦k≦a+1 divided in step S903. The (a+2)-th sub-vectory_([0]) includes sub-vectors from a first row sub-vector to the i₀-throw sub-vector of the vector y, the (a+2-k)-th sub-vector y_([k]) (where0≦k≦a) includes sub-vectors from the (i_(k−1)+1)-th row sub-vector tothe i_(k)-th row sub-vector of the vector y, and the first sub-vectory_([a+1]) includes sub-vectors from the i_(a)-th row sub-vector to M-throw sub-vector of the vector y (step S905).

FIG. 18 is a flowchart illustrating a step of detecting the latticepoint by using the division algorithm shown in FIG. 17.

Referring to FIG. 18, when it is assumed that the number of rowsincluded in the upper triangular matrix R is M, the upper triangularmatrix R is divided by the (a+1) number of natural numbers i₀, i₁, . . ., i_(a) (where 1≦i₀<i₁< . . . <i_(a)<M) (step S1001). This is the sameas the division step shown in FIG. 17.

Next, a lattice point v(a+1) that is close to the divided sub-vector towhich the value of the product of the sub-upper triangular matrix R[a+1]corresponds is obtained (step S1003). Here, the lattice point v(a+1)includes M−i_(a) number of coordinates, and each of the coordinates is avector that is one of the finite number of signal values determined bythe modulation method used. In order to detect the lattice point v(a+1),one of the near ML algorithms such as the sphere decoding algorithm orthe M algorithm is used.

Next, it is assumed that i⁻¹=0 (step S1005) and an initial value of k isset to a (step S1007). And then, the column vector

$w = \begin{bmatrix}{v\left( {k + 1} \right)} \\\vdots \\{v\left( {a + 1} \right)}\end{bmatrix}$in which the v(k+1)-th column vector to the v(a+1)-th column vector aresequentially arranged is obtained (step S1009).

Next, the (a+2-k)-th transformed sub-vector y′_([k]) is obtained byeliminating the value of a product of the column vector w and thesubmatrices from the (i_(k)−i_(k−1)+1)-th column to the (M−i_(k−1))-thcolumn of the sub-upper triangular matrix R[k] from the (a+2-k)-thsub-vector y_([k]). That is, the (a+2-k)-th transformed sub-vectory′_([k]) includes signals obtained by calculating the numerical formula

$y_{j}^{\prime} = {y_{j} - {\sum\limits_{{i_{k} + 1} \leq l \leq M}{{R\lbrack k\rbrack}_{j{({l - i_{k - 1}})}}w_{l - i_{k}}}}}$with respect to all j (where i_(k−1)+1≦j≦i_(k)). The lattice point v(k)in which the value of a product of the desired lattice point and thesubmatrices that include elements from the first column to the(i_(k)−i_(k−1))-th column of the sub-upper triangular matrix R[k] withrespect to the (a+2-k)-th transformed sub-vector y′_([k]) in distancebecomes the smallest value is detected (step S1011).

That is, the lattice point v(k) in which the distance between [y′_(i)_(k−1) ₊₁ y′_(i) _(k−1) ₊₂ . . . y′_(i) _(k) ]^(t) andR[k](1:i_(k)−i_(k−1))v(k) is sufficiently small is obtained. Here, thelattice point v(k) includes the i_(k)−i_(k−1) number of coordinates, andeach of the coordinates is one vector that is one of the finite numberof signals determined by the used modulation method. Further, the matrixR[k](1:i_(k)−i_(k−1)) is composed from the first column to the(i_(k)−i_(k−1))-th column of the matrix R[k]. In order to detect thelattice point v(k), one of the near ML algorithms such as the spheredecoding algorithm or the M algorithm is used as the case of detectingthe lattice point v(a+1).

Next, k−1 is substituted to k in the obtained lattice point v(k) (stepS1013).

Next, k and 0 are compared in the obtained lattice point v(k) (stepS1015). If the k is equal to or larger than 0, the procedure is branchedto step S1009. If the k is smaller than 0 (that is, k is equal to −1),

$\left\lbrack \left. \quad\begin{matrix}\begin{matrix}{v(0)} \\{v(1)}\end{matrix} \\\vdots \\{v\left( {a + 1} \right)}\end{matrix} \right\rbrack \right.$is output (step S1017).

FIG. 19 is a flowchart illustrating another method of detecting thelattice point to which the division algorithm shown in FIG. 17 isapplied.

Referring to FIG. 19, when it is assumed that the number of rowsincluded in the upper triangular matrix R is M, the upper triangularmatrix R is divided on the basis of the (a+1) number of natural numbersi₀, i₁, . . . , i_(a) (where 1≦i₀<i₁< . . . <i_(a)<M) (step S1101).

Next, a plurality of (n_(a+1) number on lattice points v in which thevalue of a product of the sub-upper triangular matrix R[a+1] and adesired lattice point v is equal to or less than the predeterminedreference value with respect to the sub-vector y_([k]) in distance andthe corresponding distance are calculated (step S1103). That is, n_(a+1)number of lattice points v in which the value resulting from thenumerical formula d(v)=∥[y_(i) _(a) ₊₁ . . . y_(M)]^(t)−R[a+1]v∥²corresponds to the sufficiently small and the d(•) values at thecorresponding lattice points are obtained and stored. It is assumed thatthe symbol Σ denotes the set of n_(a+1) number of points v. When thesphere decoding algorithm is used to obtain the value of the set Σ, theset Σ is composed of a point having the smallest d(•) value andn_(a+1)−1 number of points having the d(•) value that is immediatelylarger than the smallest d(•) value.

Next, i⁻¹=0 and k=a are set (S1105, S1107).

Next, in a case of a vector in which the lattice point v is an elementof the set Σ and the lattice point u includes (i_(k)−i_(k−1)) number ofcoordinates each of which are a vector being one of the finite numbersignal values determined by the used modulation method, n_(k) number oflattice points corresponding to a vector

$\left\lbrack \left. \quad\begin{matrix}u \\v\end{matrix} \right\rbrack \right.$having the sufficiently small

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value are obtained using the following Equation 14 (step S1109).

$\begin{matrix}{{d\left( \begin{bmatrix}u \\v\end{bmatrix} \right)}:={{d( v)} + {{\left\lbrack {y_{i_{k - 1} + 1}y_{i_{k - 1} + 2}\mspace{14mu}\ldots\mspace{14mu} y_{i_{k}}} \right\rbrack^{t} - {{R\lbrack k\rbrack}\left( {i_{k} - i_{k - 1} + {\left. \quad{1:{M - i_{k - 1}}} \right)v} - {{R\lbrack k\rbrack}\left( {1:{i_{k} - i_{k - 1}}} \right)u}} \right.^{2}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

That is, when the lattice point v is an element of the set Σ and a setof a plurality of lattice points having the sufficiently small

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value is denoted as Λ_(k)(v), values in the Λ_(k)(v) are stored.Λ_(k)(v) is composed of a point having the smallest

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value and a plurality of points having the

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value that is immediately larger than the smallest

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value.

At this time, when detecting the points included in the Λ_(k)(v), thepoint v is fixed as any point included in the set Σ. Further, thelattice points corresponding to the lattice point u are obtained usingone of the methods (near ML methods) that have a similar maximumlikelihood detection performance such as the sphere decoding algorithmor the M algorithm. At this time, a predetermined number of pointsincluding a point having the smallest value resulting from the formula∥[y_(i) _(k−1) ₊₁ y_(i) _(k−1) ₊₂ . . . y_(i) _(k)]^(t)−R[k](i_(k)−i_(k−1)+1:M−i_(k−1))v−R[k](1:i_(k)−i_(k−1))u∥² areobtained. With respect to all points included in the set Σ, n_(k) numberof points having the small

$d\left( \left\lbrack {\quad\begin{matrix}u \\v\end{matrix}} \right\rbrack \right)$value in the

$\bigcup\limits_{v \in \Sigma}{\Lambda_{k}(v)}$obtained after the Λ_(k)(v) is calculated are selected and the selectedpoints are set as elements of the set Σ.

Next, k−1 is substituted to k (step S1111).

Then, it is determined whether k is equal to or larger than 0 (stepS1113). When k is equal to or larger than 0, the process (Equation 14)proceeds to step S1109. When k is smaller than 0, that is, k is −1, thelattice points corresponding to Λ_(k) are output (step S1115). At thistime, in a case of the soft decision being performed, it is set as n₀=1.When calculating the LLR, it is set as n₀>1.

On the other hand, even though not shown in the drawing, a method ofdetecting a transmission signal to which the above-described divisiondetection method is applied to the predetermined L number of receivedsignal vectors may be applied to a multi-step decoder. In this case, thebasic flow is similar, but in the method of detecting a transmissionsignal applied to a multi-step decoder, a matrix that indicates achannel state estimated with respect to each of the plurality ofreceived signals Y is used and may includes the following.

First, an example of dividing the upper triangular matrix R by two willbe described. At this time, repeated descriptions will be omitted andjust examples of the dividing step (step S107) and the detecting step(step S109) will be described.

In the step of dividing the upper triangular matrix R, each of theplurality of upper triangular matrices R_({l}), 1≦l≦L are divided intothe first sub-upper triangular matrices bR_({l})[i₀], 1≦l≦L which is the(M−i₀)×(M−i₀) submatrix that includes elements from the (i₀+1)-th columnto the M-th column among from the (i₀+1)-th row to the M-th row and thesecond sub-upper triangular matrix uR_({l})[i₀], 1≦l≦L which is the(i₀×M) submatrix that includes elements from the first column to theM-th column from among the first row to the i₀-th row based on thepredetermined row i₀ determined on the basis of the SNR or the number ofrows.

Next, each of the vectors y^({l}), 1≦l≦L is divided into the firstsub-vector y_([1]) ^({l}) and the second sub-vector y_([2]) ^({l}) so asto correspond to the divided first sub-upper triangular matrixbR_({l})[i₀] and the second sub-upper triangular matrix uR_({l})[i₀],respectively. The first sub-vector y_([1]) ^({l}), 1≦l≦L is a sub-vectorthat includes elements from the (i₀+1)-th row to the M-th row of thevector y^({l}) and the second sub-vector y_([2]) ^({l}), 1≦l≦L is asub-vector that includes elements from the first row to the i₀-th row ofthe vector y^({l}).

Next, the lattice point v^({l}) in which the value of a product of thefirst sub-upper triangular matrix bR_({l})[i₀], 1≦l≦L and the latticepoint is the closest to the first sub-vector y_([1]) ^({l}) in distanceis detected.

Then, the value of a product of the submatrix that includes elementsfrom the (i₀+1)-column to the M-th column of the second sub-uppertriangular matrix uR_({l})[i₀], 1≦l≦L and the lattice point v^({l}) iseliminated from the second sub-vector y_([2]) ^({l}) so as to obtain thetransformed second sub-vector y′_([2]) ^({l}).

The lattice point u^({t}) in which the value of product of the latticepoint and the submatrix that includes elements from the first column tothe i₀-the column of the second sub-upper triangular matrixuR_({l})[i₀], 1≦l≦L with respect to the transformed second sub-vectory′_([2]) ^({l}) in distance is the closest is then detected.

Thereafter, the log-likelihood ratio LLR_(i+i) ₀ _(,k) ^({l}) of thek-th bit of the (i+i₀)-th bit string of the vector y^({l}), 1≦l≦L andthe log-likelihood ratio LLR_(i,k) ^({l}) of the k-th bit of the bitstring corresponding to the i-th signal may be calculated using each thefirst sub-upper triangular matrix bR_({l})[i₀], 1≦l≦L and the secondsub-upper triangular matrix uR_({l})[i₀], 1≦l≦L.

More particular, the log-likelihood ratio LLR_(i+i) ₀ _(,k) ^({l}) ofthe k-th bit of the (i+i₀)-th bit string of the vector y^({l)}, 1≦l≦L iscalculated using the first sub-upper triangular matrix bR_({l}[i) ₀].

The lattice point v^({l})=[v₁ ^({l}) . . . v_(M−i) ₀ ^({l})] is obtainedby decoding each of the repeatedly calculated log-likelihood ratiosLLR_(i+i) ₀ _(,k) ^({l}) (where 1≦l≦L).

The log-likelihood ratio LLR_(i,k) ^({l}) of the k-th bit of the bitstring corresponding to the i-th signal is calculated using the obtainedlattice point v^({l})=[v₁ ^({l}) . . . v_(M−i) ₀ ^({l})] and the secondsub-upper triangular matrix uR_({l})[i₀].

Next, an example of dividing the upper triangular matrix R into aplurality of submatrices will be described.

Each of the plurality of upper triangular matrices R_({l}), 1≦l≦L aredivided into a plurality of sub-upper triangular matrices R_({l})[k](where k is a+1, . . . , 1, 0) based on the predetermined row i₀, i₁, .. . i_(a), 1≦i₀<i₁< . . . <i_(a)<M determined on the basis of the SNR orthe number of rows as follows:

R_({l})[a + 1]_(ij) := R_({l}(i_(a) + i)(i_(a) + j)), 1 ≤ i, j ≤ M − i_(a)R_({l})[a]_(ij) := R_({l}(i_(a − 1) + i)(i_(a − 1) + j)), 1 ≤ i ≤ i_(a) − i_(a − 1), 1 ≤ j ≤ M − i_(a − 1)⋮R_({l})[k]_(ij) := R_({l}(i_(k − 1) + i)(i_(k − 1) + j)), 1 ≤ i ≤ i_(k) − i_(k − 1), 1 ≤ j ≤ M − i_(k − 1)⋮R_({l})[1]_(ij) := R_({l}(i₀ + i)(i₀ + j)), 1 ≤ i ≤ i₁ − i₀, 1 ≤ j ≤ M − i₀R_({l})[0]_(ij) := R_({l}ij), 1 ≤ i ≤ i₀, 1 ≤ j ≤ M

Next, the vector y^({l}) is divided into a plurality of sub-vectorsy^({l})[k] (where k is a+1, . . . , 1, 0) so as to correspond to each ofthe plurality of sub-upper triangular matrices R_({l})[k] (where k isa+1, . . . , 1, 0). That is, the vector y^({l})[a+1] is a vector thatincludes elements from the (i_(a)+1)-row to the m-th row of the vectory^({l}). When k represents one of a, . . . , 1, 0, the vector y^({l})[k]is a vector that includes elements from the (i_(k−1)+1)-th row to thei_(k)-th row of the vector y^({l}), and the vector y^({l})[0] is avector that includes elements from the first row to the i₀-th row of thevector y^({l}).

Next, the log-likelihood ratio vector is obtained using the max-log mapalgorithm on the basis of the sub-upper triangular matrix R_({l})[a+1](where 1≦l≦L) and the vector y^({l})[a+1] (where 1≦l≦L). The obtainedlog-likelihood ratio vector is decoded so as to obtain the lattice pointv^({l})[a+1] (where 1≦l≦L).

When an initial value of k is set to a and the value of k sequentiallydecreases until the value of k reaches 0, the transformed sub-vectory′^({l})[k] (where 1≦1≦L) is obtained by eliminating the value of theproduct of the sub-vector

$\left\lbrack \left. \quad\begin{matrix}{v^{\{ l\}}\left\lbrack {k + 1} \right\rbrack} \\\vdots \\{v^{\{ l\}}\left\lbrack {a + 1} \right\rbrack}\end{matrix} \right\rbrack \right.$and the submatrix that includes elements from a (i_(k)−i_(k−1)+1)-thcolumn to a (M−i_(k−1))-th column of the sub-upper triangular matrixR_({l})[k] (where 1≦1≦L) from the sub-vector y^({l})[k] (where 1≦1≦L).

The above-described exemplary embodiments of the present invention arenot limited to the above-described method and apparatus. The inventionmay be implemented by a program that causes implementation of functionscorresponding to the structure of the exemplary embodiments of thepresent invention or a recording medium storing the program, and may beeasily implemented on the basis of the above-described exemplaryembodiments.

It is to be understood that the invention is not limited to thedisclosed embodiments, but, on the contrary, is intended to covervarious modifications and equivalent arrangements included within thespirit and scope of the appended claims.

According to the embodiments described above, there are advantages thatthe calculation process may be partially adjusted in accordance withtarget signal detection accuracy.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

What is claimed is:
 1. A computer-implemented method of detecting a transmission signal from a received signal in a multiple input multiple output (MIMO) system, the method comprising executing computer program code instructions to cause one or more computer processors to: obtain a unitary matrix Q and a triangular matrix R by performing a sorted QR-decomposition (SQRD) algorithm with respect to a matrix B indicating a channel state; calculate a vector y by multiplying a transpose matrix Q^(t) of the unitary matrix Q by the received signal Y; divide the triangular matrix R into a plurality of sub triangular matrices; and divide the calculated vector y into a plurality of sub-vectors so as to correspond to the divided plurality of sub triangular matrices; and detect a lattice point corresponding to each of the divided sub-vectors using the divided plurality of sub triangular matrices.
 2. The method of detecting a transmission signal of claim 1, wherein the triangular matrix R is an upper triangular matrix and dividing of the upper triangular matrix R includes: dividing the upper triangular matrix R into a first sub-upper triangular matrix bR[i₀] which is a (M−i₀)×(M−i₀) matrix and a second sub-upper triangular matrix uR[i₀] which is a (i₀×M) matrix on the basis of a predetermined row i₀ determined on the basis of a signal-to-noise ratio (SNR) or the number of rows; and dividing the vector y into a first sub-vector y_([1]) and a second sub-vector y_([2]) so as to correspond to the divided first sub-upper triangular matrix bR[i₀] and the second sub-upper triangular matrix uR[i₀], respectively.
 3. The method of detecting a transmission signal of claim 2, wherein the first sub-upper triangular matrix bR[i₀], in a matrix composed of row vectors that include elements from an (i₀+1)-th row to which the predetermined row is increased by one to an M-th row which is the last row of the upper triangular matrix R, is an (M−i₀)×(M−i₀) matrix composed of column vectors corresponding to column numbers larger than i₀+1; and the second sub-upper triangular matrix uR[i₀] is an (i₀×M) matrix composed of row vectors that include elements from a first row to an i₀-th row of the upper triangular matrix R.
 4. The method of detecting a transmission signal of claim 2, wherein the detecting of the lattice point includes: detecting a lattice point v in which a value of a product of the first sub-upper triangular matrix bR[i₀] and the lattice point v in distance is the closest to the first sub-vector; obtaining a transformed second sub-vector y′_([2]) by eliminating the value of a product of the submatrix that includes elements from the (i₀+1)-th column to the M-th column of the second sub-upper triangular matrix uR[i₀] the lattice point v from the second sub-vector y_([2]); and detecting a lattice point u in which the value of a product of the submatrix that includes elements from the first column to the i₀-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point u in distance is the closest to the transformed second sub-vector y′_([2]).
 5. The method of detecting a transmission signal of claim 4, further comprising: after the detecting of the lattice point, calculating a log-likelihood ratio (LLR) corresponding to the first sub-vector y_([1]) using the lattice point v and a max-log map algorithm; and calculating a log-likelihood ratio corresponding to the second sub-vector y_([2]) using the lattice point u and the max-log map algorithm.
 6. The method of detecting a transmission signal of claim 5, wherein the calculating of the log-likelihood ratio corresponding to the second sub-vector y_([2]) includes, with respect to each k-th bit of a bit string of an (i+i₀)-th signal (where 1≦i≦M−i₀) of the signal transmission vector: inverting a value of the k-th bit of the bit string corresponding to an i-th signal of the lattice point v; obtaining the lattice point v(i,k) in which the value of a product of the first sub-upper triangular matrix bR[i₀] and the lattice point with respect to the first sub-vector y_([1]) in distance is the closest from among (M−i₀)-degree lattice points having the bit value obtained by inverting the value of the k-th bit as a bit value of the k-th bit of the bit string of the i-th signal; and obtaining the log-likelihood ratio LLR_(i+i) ₀ _(,k) of the k-th bit of the bit string corresponding to the (i+i₀)-th signal of the signal transmission vector corresponding to the vector y using a difference between a value of the obtained lattice point v(i,k) and a value of the product of the first sub-upper triangular matrix bR[i₀] and the lattice point v with respect to the first sub-vector y_([1]) in distance.
 7. The method of detecting a transmission signal of claim 5, wherein the calculating of the log-likelihood ratio, with respect to each i (where 1≦i≦i₀) of the k-th bit of the bit string of the i-th signal of the signal transmission vector, includes: inverting a value of the k-th bit of the bit string corresponding to the i-th signal of the lattice point u; obtaining a lattice point ū(i,k) in which a value of a product of the submatrix that includes elements from a first column to an i₀-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point with respect to the transformed second sub-vector y′_([2]) in distance is the closest from among i₀-degree lattice points having the inverted bit value as a value of the k-th bit of the bit string of the i-th bit string; and obtaining a log-likelihood ratio LLR_(i,k), as a corresponding value of distance of the obtained lattice point ū(i,k), of the k-th bit of the bit string corresponding to the i-th signal of the signal transmission vector corresponding to the vector y using a difference between a value of a product of the submatrix that includes elements from the first column to the i₀-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point ū(i,k) with respect to the transformed second sub-vector y′_([2]) in distance and a value of a product of the submatrix that includes elements from the first column to the i₀-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point u with respect to the transformed second sub-vector y′_([2]) in distance.
 8. The method of detecting a transmission signal of claim 2, wherein the detecting of the lattice point includes: detecting a plurality of lattice points v[l] in which a value of a product of the first sub-upper triangular matrix uR[i₀] and the desired lattice point with respect to the first sub-vector y′_([1]) in distance is less than a predetermined reference value; obtaining a plurality of transformed second sub-vectors y′_([2])[l] by eliminating a value of a product of the submatrix that includes elements from the (i₀+1)-th column to the M-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point v[l] from the second sub-vector y_([2]) by using the plurality of lattice points v[l]; detecting the lattice point u[l] in which the value of a product of the submatrix that includes elements from the first column to the i₀-th column of a second sub-upper triangular matrix uR[i₀] and the desired lattice point with respect to each of the plurality of transformed second sub-vectors y′_([2])[l] in distance becomes the smallest; and selecting a lattice point $\left\lbrack \left. \quad\begin{matrix} {u\left\lbrack l_{0} \right\rbrack} \\ {v\left\lbrack l_{0} \right\rbrack} \end{matrix} \right\rbrack \right.$ in which a corresponding value of distance with respect to the plurality of lattice points $\left\lbrack \left. \quad\begin{matrix} {u\lbrack l\rbrack} \\ {v\lbrack l\rbrack} \end{matrix} \right\rbrack \right.$ that include the detected plurality of lattice points v[l] and the detected lattice point u[l] becomes the smallest, the value of distance being a sum of a value of a product of the first sub-upper triangular matrix bR[i₀] and the lattice point v[l] with respect to the first sub-vector y_([1]) in distance and a value of a product of the submatrix that includes elements from the first column to the i₀-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point u[l] with respect to the transformed second sub-vector y′_([2])[l] in distance.
 9. The method of detecting a transmission signal of claim 2, wherein the detecting of the lattice point includes: detecting a plurality of (m number of) lattice points v[l] in which the product of the first sub-upper triangular matrix bR[i₀] and the lattice point with respect to the first sub-vector y_([1]) in distance is equal to or less than a predetermined reference value; obtaining the plurality of (m number of) transformed second sub-vectors y′₂[l] by eliminating a value of a product of the submatrix that includes elements from the (i₀+1)-th column to the M-th column of the second sub-upper triangular matrix uR[i₀] and the lattice point v[l] from the second sub-vector y_([2]) using the plurality of (m number of) lattice points v[l]; and detecting a plurality of lattice points u[l][h] in which the product of the submatrix that includes elements from the first column to the i₀-th column of the second sub-upper triangular matrix uR[i₀] and the plurality of (m number of) transformed second sub-vectors y′₂[l] in distance is equal to or less than the predetermined reference value.
 10. The method of detecting a transmission signal of claim 2, further comprising: after the detecting of the lattice point, calculating the log-likelihood ratio LLR_(i,k) of the k-th bit x_(i,k) of the bit string corresponding to the i-th signal by using a sum ${f\begin{pmatrix} {{u\lbrack l\rbrack}\lbrack h\rbrack} \\ {v\lbrack l\rbrack} \end{pmatrix}} = {{{\overset{\_}{d}}_{l}\left( {{u\lbrack l\rbrack}\lbrack h\rbrack} \right)} + {d\left( {v\lbrack l\rbrack} \right)}}$  of each value of distance calculated with respect to the detected plurality of lattice points $\left\lbrack \left. \quad\begin{matrix} {{u\lbrack l\rbrack}\lbrack h\rbrack} \\ {v\lbrack l\rbrack} \end{matrix} \right\rbrack \right.$  and a value α(i,k) to which the log operation is performed with respect to a previous probability ratio of each bit.
 11. The method of detecting a transmission signal of claim 1, wherein the triangular matrix R is an upper triangular matrix and the dividing of the upper triangular matrix R and dividing the calculated vector y include: dividing the upper triangular matrix R into a plurality of sub-upper triangular matrices R[k] (where 0≦k≦a+1) on the basis of a plurality of predetermined rows (i₀, i₁, . . . , i_(a), 1≦i₀<i₁< . . . <i_(a)<M, where M indicates the entire number of rows of the upper triangular matrix R) determined on the basis of the SNR or the number of rows using the following equation, R[a + 1]_(ij) := R_((i_(a) + i)(i_(a) + j)), 1 ≤ i, j ≤ M − i_(a) R[a]_(ij) := R_((i_(a − 1) + i)(i_(a − 1) + j)), 1 ≤ i ≤ i_(a) − i_(a − 1), 1 ≤ j ≤ M − i_(a − 1) ⋮ R[k]_(ij) := R_((i_(k − 1) + i)(i_(k − 1) + j)), 1 ≤ i ≤ i_(k) − i_(k − 1), 1 ≤ j ≤ M − i_(k − 1) ⋮ R[1]_(ij) := R_((i₀ + i)(i₀ + j)), 1 ≤ i ≤ i₁ − i₀, 1 ≤ j ≤ M − i₀ R[0]_(ij) := R_(ij), 1 ≤ i ≤ i₀, 1 ≤ j ≤ M;   and dividing the vector y into a plurality of sub-vectors y_([k]) (where 0≦k≦a+1) so as to correspond to the divided plurality of sub-upper triangular matrices R[k] (where 0≦k≦a+1), in which an (a+2)-th sub-vector y_([0]) includes elements from a first row to the i₀-th row of the vector y, an (a+2-k)-th sub-vector y_([k]) (where 1≦k≦a) includes elements from an (i_(k−1)+1)-th row to an (i_(k))-th row of the vector y, and the first sub-vector y_(|a+1|) includes elements from an i_(a)-th row to the M-th row of the vector y.
 12. The method of detecting a transmission signal of claim 11, wherein the detecting of the lattice point further includes: obtaining a lattice point v(a+1) in which a value of a product of the sub-upper triangular matrix R[a+1] and the desired lattice point is closest to the first sub-vector y_([a+1]); substituting a to k as an initial value when i⁻¹=0; obtaining a column vector $w = \begin{bmatrix} {v\left( {k + 1} \right)} \\ \vdots \\ {v\left( {a + 1} \right)} \end{bmatrix}$  in which column vectors corresponding from a {v(k+1)}-th column to a {^(v(a+1))}-th column are sequentially arranged as the obtained vectors; obtaining the (a+2-k)-th transformed sub-vector y′_([k]) by eliminating a value of a product of the submatrix that includes elements from an (i_(k)−i_(k−1)+1)-th column to an (M−i_(k−1))-th column of the sub-upper triangular matrix R[k] and the column vector w from the (a+2-k)-th sub-vector y_([k]); obtaining the lattice point v^((k)) in which a value of a product of the submatrix that includes elements from the first column to a (i_(k)−i_(k−1))-th column of the sub-upper triangular matrix R[k] and the desired lattice point is the smallest with respect to the (a+2-k)-th sub-vector y_([k]) in distance; and substituting k−1 into k and repeating the obtaining of the column vector $w = \begin{bmatrix} {v\left( {k + 1} \right)} \\ \vdots \\ {v\left( {a + 1} \right)} \end{bmatrix}$  to the obtaining of the lattice point v(k) if k is equal to or larger than 0 and outputting a lattice point $\left\lbrack \left. \quad\begin{matrix} {v(0)} \\ {v(1)} \\ \vdots \\ {v\left( {a + 1} \right)} \end{matrix} \right\rbrack \right.$  if k is −1.
 13. The method of detecting a transmission signal of claim 11, wherein the detecting of the lattice point further includes: obtaining the plurality of (n_(a+1) number of) lattice points v in which a value of a product of the sub-upper triangular matrix R[a+1] and the desired lattice point with respect to the first sub-vector y_([a+1]) is less than the predetermined reference value and a value of a corresponding distance d(v), and defining a set of the plurality of (n_(a+1) number of) lattice points v as Σ; substituting a to k as an initial value when i⁻¹=0. detecting a plurality of lattice points u with respect to the lattice points v included in the set Σ, a sum of a value of a product of the submatrix that includes elements from an {(i_(k)−i_(k−1))+1}-th column to an (M−i_(k−1))-th column of the sub-upper triangular matrix R[k] and the lattice point v and a value of a product of the submatrix that includes elements from the first column to an (i_(k)−i_(k−1))-th column of the sub-upper triangular matrix R[a+1] and the lattice point u being equal to or less than a predetermined reference value with respect to a value of distance d(u) on the basis of the (a+2-k)-th sub-vector y_([k]), and simultaneously detecting n_(k) number of lattice points $\left\lbrack \left. \quad\begin{matrix} u \\ v \end{matrix} \right\rbrack \right.$  in which a sum of a value of a distance d(v) and a value of a distance d(u) is equal to or less than the predetermined reference value; defining the sum of the value of the distance d(v) and the value of the distance d(u) as $d\left( \begin{bmatrix} u \\ v \end{bmatrix} \right)$  and defining a set of the n_(k) number of lattice points $\left\lbrack \left. \quad\begin{matrix} u \\ v \end{matrix} \right\rbrack \right.$  as Σ; and substituting k−1 to k and repeating the detecting of the plurality of lattice points u and the defining when k is equal to or larger than 0 or outputting the set Σ when k is −1.
 14. The method of detecting a transmission signal of claim 1, wherein the process of obtaining the unitary matrix Q and the upper triangular matrix R decomposes $\left\lbrack \left. \quad\begin{matrix} B \\ {\sigma\; I_{M}} \end{matrix} \right\rbrack \right.$ by the SQRD algorithm where σ is the reciprocal of the square root of a signal-to-noise ratio measured in a receiving terminal of the MIMO system and I_(M) is the identity matrix with the size of the signal vector to be detected.
 15. The method of detecting a transmission signal of claim 1, wherein the process of obtaining the unitary matrix Q and the upper triangular matrix R rearranges the columns of the matrix B, representing the channel state, in increasing order of the Euclidean norms of the columns and then applies QR decomposition on the rearranged matrix B.
 16. The method of detecting a transmission signal of claim 1, wherein the process of obtaining the unitary matrix Q and the upper triangular matrix R rearranges the columns of the matrix B, representing the channel state, in increasing order of the Euclidean norms of the columns and then applies QR decomposition on the matrix $\left\lbrack \left. \quad\begin{matrix} B \\ {\sigma\; I_{M}} \end{matrix} \right\rbrack \right.$ where σ is the reciprocal of the square root of a signal-to-noise ratio measured in a receiving terminal of the MIMO system and I_(M) is the identity matrix with the size of the signal vector to be detected. 